Here is the full list of all 49 BULLET SOUL INFINITE BURST achievements.
Watched a ending with Sadahl
Cleared stage 5 in normal mode
Cleared stage 4 in normal mode
Cleared stage 3 in normal mode
Break my highest score in caravan mode
Retried caravan mode
Cleared a game in caravan mode
Watched a ending with Yun
Cleared stage 5 in burst mode
Cleared stage 4 in burst mode
Increased your coins' score rate up to 100,000 points
Kept a burst for 30 seconds
Missed in caravan mode
Cleared stage 2 in normal mode
Cleared stage 1 in normal mode
Cleared stage 3 in burst mode
Cleared stage 2 in burst mode
Collide against an enemy during a burst
Play a game to get in Turtle 10000
Play a game to get in Red Hot Skull
Cleared stage 1 in burst mode
Beat a boss in a moment during a burst.
Used 2 bursts in a stage
Recovered HP
Used a burst
Cancel a burst manually
Play a game to get in Piece of Cake
Play a game to get in FA-98 Stinger
Cleared a game without missing in caravan mode
Unlocked Musou mode
Clear stage 1 in Musou mode
Clear stage 2 in Musou mode
Clear stage 3 in Musou mode
Clear stage 4 in Musou mode
Clear stage 5 in Musou mode
Watched a ending with Zenichi
Wawtched the ending with loop
Earned 50 HP items with your HP full in total
Earn 50 collection bonuses in total
Earned 25,000 coins in total
Earned Platinum Medal at stage 1 of Bancho mode
Earned Platinum Medal at stage 2 of Bancho mode
Earned Platinum Medal at stage 3 of Bancho mode
Earned Platinum Medal at stage 4 of Bancho mode
Earned Platinum Medal at stage 5 of Bancho mode
Earned Tamashii gauge 2,000 magnification in total
Earn 500 various bonuses in total.
Shot down 25,000 units in total
Earned 25 and over medals in total